Finite Group Databasebeta

← C2×#10591712 #11808156

Subgroups — C2×#10591712 #11808156

Order 1152.

3185 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#638C211yesmaximal, characteristic
2C22×C3×#217C211yesmaximal, characteristic, complemented
3C22×C3×#217C211yesmaximal, characteristic, complemented
4C22×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
5C22×#3722C211yesmaximal, characteristic, complemented
6C22×#3722C211yesmaximal, characteristic, complemented
7#10591712C218yesmaximal, direct product factor
8C2×#63579C211yesmaximal, characteristic, complemented
9C2×#4959—31nomaximal
10C2×#4961—31nomaximal
11C25×C32C2211yescharacteristic
12C24×C3⋊D3C2211yescharacteristic
13C22×#638—24no—
14C22×#638—24no—
15C22×#638—24no—
16C22×#638C2214yes—
17C23×C3⋊Dic3C2211yescharacteristic
18C23×C3×Dic3C2211yescharacteristic
19C23×C3×Dic3C2211yescharacteristic
20C23×C3×Dic3C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C2×C3×#217—24no—
23C2×C3×#217—24no—
24C2×C3×#217C2214yescomplemented
25C2×C3×#217C2214yescomplemented
26C2×Dic3⋊Dic3—24no—
27C2×Dic3⋊Dic3C2214yescomplemented
28C2×#3722—24no—
29C2×#3722—24no—
30C2×#3722C2214yescomplemented
31C2×#3722C2214yescomplemented
32#63579C2214yescomplemented
33C23×#67—31no—
34C23×#67—31no—
35C23×#67—61no—
36C22×C3×C22⋊C4—31no—
37C22×C3×C22⋊C4—31no—
38C22×#217D311yescharacteristic, complemented
39C22×#217D311yescharacteristic, complemented
40C22×(C2×D3)⋊C4—31no—
41C22×(C2×D3)⋊C4—31no—
42C22×(C2×D3)⋊C4—31no—
43C22×(C2×D3)⋊C4—31no—
44C22×C4⋊Dic3—31no—
45C22×Dic3⋊C4—31no—
46C2×C3⋊#95—31no—
47C2×C3⋊#95—31no—
48#4961—38no—
49#4959—38no—
50C24×C32—22no—
51C24×C32—22no—
52C24×C32—22no—
53C24×C32—22no—
54C24×C32—22no—
55C24×C32—22no—
56C24×C32D414yes—
57C24×C32C2312yes—
58C24×C32C2311yescharacteristic
59C23×C3⋊D3—22no—
60C23×C3⋊D3—22no—
61C23×C3⋊D3—22no—
62C23×C3⋊D3—22no—
63C23×C3⋊D3—22no—
64C23×C3⋊D3—22no—
65C23×C3⋊D3D414yes—
66C23×C3⋊D3C2312yes—
67C2×#638—232no—
68C2×#638—28no—
69C2×#638—28no—
70C2×#638—28no—
71C22×C3⋊Dic3—22no—
72C22×C3⋊Dic3—22no—
73C22×C3⋊Dic3D414yes—
74C22×C3⋊Dic3C2312yes—
75C22×C3×Dic3—22no—
76C22×C3×Dic3—22no—
77C22×C3×Dic3—22no—
78C22×C3×Dic3—22no—
79C22×C3×Dic3—22no—
80C22×C3×Dic3—22no—
81C22×C3×Dic3—22no—
82C22×C3×Dic3—22no—
83C22×C3×Dic3—22no—
84C22×C3×Dic3—22no—
85C22×C3×Dic3—22no—
86C22×C3×Dic3D414yescomplemented
87C22×C3×Dic3C2312yes—
88C22×C3×Dic3C2312yes—
89C22×C3×Dic3C2312yes—
90C22×C3×Dic3C2312yes—
91C3×#217—28no—
92C3×#217—28no—
93Dic3⋊Dic3—28no—
94#3722—28no—
95#3722—28no—
96C2×#394—91noSylow
97C25×C3—21no—
98C25×C3C2×D311yescharacteristic
99C25×C3C2×D311yescharacteristic
100C24×D3—31no—
101C24×D3—31no—
102C24×D3—61no—
103C23×C3×C4—31no—
104C23×C3×C4—31no—
105C23×C3×C4—31no—
106C23×C3×C4—31no—
107C22×#67—34no—
108C22×#67—34no—
109C22×#67—64no—
110C22×#67—64no—
111C22×#67—64no—
112C22×#67—64no—
113C22×#67—64no—
114C22×#67—68no—
115C22×#67—68no—
116C22×#67—68no—
117C22×#67—64no—
118C22×#67—64no—
119C23×Dic3—31no—
120C23×Dic3—31no—
121C23×Dic3—61no—
122C23×Dic3C2×D311yescharacteristic
123C23×Dic3C2×D311yescharacteristic
124C23×Dic3C2×D311yescharacteristic
125C23×Dic3C2×D311yescharacteristic
126C2×C3×C22⋊C4—34no—
127C2×C3×C22⋊C4—34no—
128C2×C3×C22⋊C4—64no—
129C2×C3×C22⋊C4—64no—
130C2×#217—24no—
131C2×#217—24no—
132C2×#217C2×D314yescomplemented
133C2×#217C2×D314yescomplemented
134C2×(C2×D3)⋊C4—34no—
135C2×(C2×D3)⋊C4—34no—
136C2×(C2×D3)⋊C4—34no—
137C2×(C2×D3)⋊C4—34no—
138C2×(C2×D3)⋊C4—64no—
139C2×(C2×D3)⋊C4—64no—
140C2×(C2×D3)⋊C4—64no—
141C2×(C2×D3)⋊C4—64no—
142C2×C4⋊Dic3—34no—
143C2×C4⋊Dic3—64no—
144C2×Dic3⋊C4—34no—
145C2×Dic3⋊C4—64no—
146C3⋊#95—34no—
147C3⋊#95—34no—
148C23×C32—28no—
149C23×C32—22no—
150C23×C32—22no—
151C23×C32—28no—
152C23×C32—28no—
153C23×C32—22no—
154C23×C32—22no—
155C23×C32—22no—
156C23×C32—22no—
157C23×C32—44no—
158C23×C32—44no—
159C23×C32—44no—
160C23×C32—44no—
161C23×C32C2×D414yes—
162C23×C32C2×D412yes—
163C23×C32C2×D412yes—
164C23×C32C2×D412yes—
165C23×C32C2×D412yes—
166C23×C32#4112yes—
167C23×C32#4112yes—
168C23×C32#4112yes—
169C23×C32C2411yescharacteristic
170C22×C3⋊D3—28no—
171C22×C3⋊D3—22no—
172C22×C3⋊D3—22no—
173C22×C3⋊D3—28no—
174C22×C3⋊D3—28no—
175C22×C3⋊D3—22no—
176C22×C3⋊D3—22no—
177C22×C3⋊D3—22no—
178C22×C3⋊D3—22no—
179C22×C3⋊D3—44no—
180C22×C3⋊D3—44no—
181C22×C3⋊D3—44no—
182C22×C3⋊D3—44no—
183C22×C3⋊D3C2×D414yes—
184#638—232no—
185C2×C3⋊Dic3—28no—
186C2×C3⋊Dic3—22no—
187C2×C3⋊Dic3—22no—
188C2×C3⋊Dic3C2×D414yes—
189C2×C3×Dic3—28no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—44no—
202C2×C3×Dic3—44no—
203C2×C3×Dic3—44no—
204C2×C3×Dic3C2×D414yescomplemented
205C23×D4—91no—
206C22×C4⋊C4—91no—
207C22×C22⋊C4—31no—
208C22×C22⋊C4—31no—
209C22×C22⋊C4—91no—
210C22×C22⋊C4—91no—
211#394—98no—
212C2×#95—91no—
213C24×C3—24no—
214C24×C3—24no—
215C24×C3—22no—
216C24×C3—22no—
217C24×C3—22no—
218C24×C3—22no—
219C24×C3—22no—
220C24×C3—22no—
221C24×C3—22no—
222C24×C3—22no—
223C24×C3—22no—
224C24×C3—22no—
225C24×C3—22no—
226C24×C3—22no—
227C24×C3—24no—
228C24×C3—22no—
229C24×C3—21no—
230C24×C3—42no—
231C24×C3—42no—
232C24×C3—42no—
233C24×C3—42no—
234C24×C3D1214yes—
235C24×C3#6714yes—
236C24×C3C22×D312yes—
237C24×C3C22×D312yes—
238C24×C3C22×D311yescharacteristic
239C24×C3C22×D311yescharacteristic
240C23×D3—34no—
241C23×D3—34no—
242C23×D3—32no—
243C23×D3—32no—
244C23×D3—64no—
245C23×D3—62no—
246C23×D3—64no—
247C23×D3—64no—
248C23×D3—62no—
249C23×D3—62no—
250C23×D3—62no—
251C23×D3—62no—
252C23×D3—62no—
253C23×D3—62no—
254C23×D3—62no—
255C23×D3—62no—
256C23×D3—62no—
257C23×D3—62no—
258C23×D3—62no—
259C23×D3—62no—
260C23×D3—122no—
261C23×D3—122no—
262C23×D3—122no—
263C23×D3—122no—
264C22×C3×C4—34no—
265C22×C3×C4—32no—
266C22×C3×C4—32no—
267C22×C3×C4—32no—
268C22×C3×C4—32no—
269C22×C3×C4—62no—
270C22×C3×C4—62no—
271C22×C3×C4—62no—
272C22×C3×C4—62no—
273C22×C3×C4—62no—
274C22×C3×C4—62no—
275C22×C3×C4—62no—
276C22×C3×C4—62no—
277C22×C3×C4—62no—
278C22×C3×C4—62no—
279C22×C3×C4—62no—
280C2×#67—68no—
281C2×#67—68no—
282C2×#67—68no—
283C2×#67—68no—
284C2×#67—616no—
285C2×#67—616no—
286C2×#67—664no—
287C2×#67—632no—
288C2×#67—632no—
289C2×#67—616no—
290C2×#67—68no—
291C2×#67—68no—
292C22×Dic3—22no—
293C22×Dic3—22no—
294C22×Dic3—22no—
295C22×Dic3—22no—
296C22×Dic3—22no—
297C22×Dic3—22no—
298C22×Dic3—22no—
299C22×Dic3—22no—
300C22×Dic3—22no—
301C22×Dic3—22no—
302C22×Dic3—22no—
303C22×Dic3—34no—
304C22×Dic3—34no—
305C22×Dic3—32no—
306C22×Dic3—32no—
307C22×Dic3—64no—
308C22×Dic3—62no—
309C22×Dic3—64no—
310C22×Dic3—64no—
311C22×Dic3—62no—
312C22×Dic3—62no—
313C22×Dic3—62no—
314C22×Dic3—62no—
315C22×Dic3#6714yescomplemented
316C22×Dic3C22×D312yes—
317C22×Dic3C22×D312yes—
318C22×Dic3C22×D312yes—
319C22×Dic3C22×D312yes—
320C3×C22⋊C4—68no—
321C3×C22⋊C4—68no—
322#217—28no—
323#217—28no—
324(C2×D3)⋊C4—68no—
325(C2×D3)⋊C4—68no—
326(C2×D3)⋊C4—68no—
327(C2×D3)⋊C4—68no—
328C4⋊Dic3—68no—
329Dic3⋊C4—68no—
330C22×C32—24no—
331C22×C32—24no—
332C22×C32—24no—
333C22×C32—42no—
334C22×C32—42no—
335C22×C32—42no—
336C22×C32—42no—
337C22×C32—416no—
338C22×C32#12014yes—
339C22×C32#12114yes—
340C22×C32#12114yes—
341C22×C32#12114yes—
342C22×C32#12314yes—
343C22×C32#12314yes—
344C22×C32#12414yes—
345C22×C32C22×D411yescharacteristic
346C22×C32C22×D411yescharacteristic
347C22×C32C22×D411yescharacteristic
348C22×C32C22×D411yescharacteristic
349C22×C32C2×#4111yescharacteristic
350C22×C32C2×#4111yescharacteristic
351C22×C32C2×#4111yescharacteristic
352C2×C3⋊D3—24no—
353C2×C3⋊D3—24no—
354C2×C3⋊D3—24no—
355C2×C3⋊D3—42no—
356C2×C3⋊D3—42no—
357C2×C3⋊D3—42no—
358C2×C3⋊D3—42no—
359C2×C3⋊D3—416no—
360C3⋊Dic3—24no—
361C3×Dic3—24no—
362C3×Dic3—42no—
363C3×Dic3—42no—
364C3×Dic3—42no—
365C25—91no—
366C25D3211yescharacteristic
367C22×D4—94no—
368C22×D4—184no—
369C22×D4—184no—
370C22×D4—184no—
371C23×C4—31no—
372C23×C4—31no—
373C23×C4—31no—
374C23×C4—31no—
375C23×C4—91no—
376C2×C4⋊C4—94no—
377C2×C4⋊C4—184no—
378C2×C22⋊C4—34no—
379C2×C22⋊C4—34no—
380C2×C22⋊C4—64no—
381C2×C22⋊C4—64no—
382C2×C22⋊C4—94no—
383C2×C22⋊C4—94no—
384C2×C22⋊C4—184no—
385C2×C22⋊C4—184no—
386#95—94no—
387C23×C3—24no—
388C23×C3—24no—
389C23×C3—216no—
390C23×C3—28no—
391C23×C3—28no—
392C23×C3—28no—
393C23×C3—28no—
394C23×C3—28no—
395C23×C3—28no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3—22no—
400C23×C3—22no—
401C23×C3—22no—
402C23×C3—22no—
403C23×C3—22no—
404C23×C3—22no—
405C23×C3—22no—
406C23×C3—22no—
407C23×C3—22no—
408C23×C3—21no—
409C23×C3—22no—
410C23×C3—22no—
411C23×C3—22no—
412C23×C3—22no—
413C23×C3—24no—
414C23×C3—22no—
415C23×C3—22no—
416C23×C3—22no—
417C23×C3—42no—
418C23×C3—42no—
419C23×C3—42no—
420C23×C3—42no—
421C23×C3—48no—
422C23×C3—48no—
423C23×C3—48no—
424C23×C3—48no—
425C23×C3—48no—
426C23×C3—48no—
427C23×C3—44no—
428C23×C3—44no—
429C23×C3—44no—
430C23×C3—44no—
431C23×C3—44no—
432C23×C3—44no—
433C23×C3—44no—
434C23×C3—44no—
435C23×C3C2×D1214yes—
436C23×C3C2×D1212yes—
437C23×C3#23512yes—
438C23×C3#23512yes—
439C23×C3#23512yes—
440C23×C3D3×D412yes—
441C23×C3D3×D412yes—
442C23×C3D3×D412yes—
443C23×C3D3×D412yes—
444C23×C3D3×D412yes—
445C23×C3#23712yes—
446C23×C3#23712yes—
447C23×C3#23712yes—
448C23×C3C2×#6714yes—
449C23×C3C2×#6712yes—
450C23×C3C2×#6712yes—
451C23×C3C23×D311yescharacteristic
452C23×C3C23×D311yescharacteristic
453C22×D3—34no—
454C22×D3—34no—
455C22×D3—64no—
456C22×D3—64no—
457C22×D3—64no—
458C22×D3—616no—
459C22×D3—68no—
460C22×D3—68no—
461C22×D3—68no—
462C22×D3—68no—
463C22×D3—68no—
464C22×D3—68no—
465C22×D3—62no—
466C22×D3—62no—
467C22×D3—62no—
468C22×D3—62no—
469C22×D3—62no—
470C22×D3—62no—
471C22×D3—62no—
472C22×D3—62no—
473C22×D3—62no—
474C22×D3—62no—
475C22×D3—62no—
476C22×D3—62no—
477C22×D3—122no—
478C22×D3—122no—
479C22×D3—122no—
480C22×D3—122no—
481C22×D3—128no—
482C22×D3—128no—
483C22×D3—128no—
484C22×D3—128no—
485C22×D3—128no—
486C22×D3—128no—
487C22×D3—124no—
488C22×D3—124no—
489C22×D3—124no—
490C22×D3—124no—
491C22×D3—124no—
492C22×D3—124no—
493C22×D3—124no—
494C22×D3—124no—
495C2×C3×C4—34no—
496C2×C3×C4—68no—
497C2×C3×C4—62no—
498C2×C3×C4—62no—
499C2×C3×C4—62no—
500C2×C3×C4—62no—
501C2×C3×C4—62no—
502C2×C3×C4—62no—
503C2×C3×C4—62no—
504C2×C3×C4—62no—
505C2×C3×C4—62no—
506C2×C3×C4—62no—
507C2×C3×C4—62no—
508C2×C3×C4—124no—
509C2×C3×C4—124no—
510C2×C3×C4—124no—
511#67—664no—
512#67—632no—
513#67—632no—
514C2×Dic3—28no—
515C2×Dic3—22no—
516C2×Dic3—22no—
517C2×Dic3—22no—
518C2×Dic3—22no—
519C2×Dic3—22no—
520C2×Dic3—22no—
521C2×Dic3—22no—
522C2×Dic3—22no—
523C2×Dic3—22no—
524C2×Dic3—22no—
525C2×Dic3—22no—
526C2×Dic3—34no—
527C2×Dic3—34no—
528C2×Dic3—44no—
529C2×Dic3—44no—
530C2×Dic3—44no—
531C2×Dic3—64no—
532C2×Dic3—64no—
533C2×Dic3—64no—
534C2×Dic3—616no—
535C2×Dic3—68no—
536C2×Dic3—68no—
537C2×Dic3—62no—
538C2×Dic3—62no—
539C2×Dic3—62no—
540C2×Dic3—62no—
541C2×Dic3C2×#6714yescomplemented
542C2×C32—44no—
543C2×C32#39418yescomplemented
544C2×C32C2×#12011yescharacteristic
545C2×C32C2×#12111yescharacteristic
546C2×C32C2×#12111yescharacteristic
547C2×C32C2×#12111yescharacteristic
548C2×C32C2×#12311yescharacteristic
549C2×C32C2×#12311yescharacteristic
550C2×C32C2×#12411yescharacteristic
551C3⋊D3—44no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—92no—
559C24—94no—
560C24—182no—
561C24—182no—
562C24—182no—
563C24—182no—
564C24—182no—
565C24—182no—
566C24#62614yes—
567C24C2×D3212yes—
568C24C2×D3211yescharacteristic
569C2×D4—188no—
570C2×D4—188no—
571C2×D4—1832no—
572C2×D4—188no—
573C22×C4—32no—
574C22×C4—34no—
575C22×C4—32no—
576C22×C4—32no—
577C22×C4—32no—
578C22×C4—62no—
579C22×C4—62no—
580C22×C4—62no—
581C22×C4—62no—
582C22×C4—62no—
583C22×C4—62no—
584C22×C4—62no—
585C22×C4—62no—
586C22×C4—62no—
587C22×C4—62no—
588C22×C4—62no—
589C22×C4—92no—
590C22×C4—94no—
591C22×C4—182no—
592C22×C4—182no—
593C4⋊C4—188no—
594C22⋊C4—68no—
595C22⋊C4—68no—
596C22⋊C4—188no—
597C22⋊C4—188no—
598C22×C3—28no—
599C22×C3—24no—
600C22×C3—24no—
601C22×C3—24no—
602C22×C3—24no—
603C22×C3—24no—
604C22×C3—24no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—24no—
613C22×C3—24no—
614C22×C3—24no—
615C22×C3—24no—
616C22×C3—24no—
617C22×C3—24no—
618C22×C3—24no—
619C22×C3—44no—
620C22×C3—44no—
621C22×C3—44no—
622C22×C3—44no—
623C22×C3—44no—
624C22×C3—44no—
625C22×C3—432no—
626C22×C3—416no—
627C22×C3—416no—
628C22×C3—42no—
629C22×C3—42no—
630C22×C3—42no—
631C22×C3—42no—
632C22×C3—42no—
633C22×C3—42no—
634C22×C3—42no—
635C22×C3—42no—
636C22×C3#88214yes—
637C22×C3#88314yes—
638C22×C3#88314yes—
639C22×C3#88414yes—
640C22×C3#88414yes—
641C22×C3#88514yes—
642C22×C3#88514yes—
643C22×C3#88614yes—
644C22×C3#92914yes—
645C22×C3#93014yes—
646C22×C3#93714yes—
647C22×C3#93814yes—
648C22×C3#93914yes—
649C22×C3#93914yes—
650C22×C3C22×D1211yescharacteristic
651C22×C3C2×#23511yescharacteristic
652C22×C3C2×#23511yescharacteristic
653C22×C3C2×#23511yescharacteristic
654C22×C3C2×D3×D411yescharacteristic
655C22×C3C2×D3×D411yescharacteristic
656C22×C3C2×D3×D411yescharacteristic
657C22×C3C2×D3×D411yescharacteristic
658C22×C3C2×D3×D411yescharacteristic
659C22×C3C2×#23711yescharacteristic
660C22×C3C2×#23711yescharacteristic
661C22×C3C2×#23711yescharacteristic
662C22×C3C22×#6711yescharacteristic
663C22×C3C22×#6711yescharacteristic
664C2×D3—68no—
665C2×D3—64no—
666C2×D3—64no—
667C2×D3—64no—
668C2×D3—64no—
669C2×D3—64no—
670C2×D3—64no—
671C2×D3—124no—
672C2×D3—124no—
673C2×D3—124no—
674C2×D3—124no—
675C2×D3—124no—
676C2×D3—124no—
677C2×D3—1232no—
678C2×D3—1216no—
679C2×D3—1216no—
680C2×D3—122no—
681C2×D3—122no—
682C2×D3—122no—
683C2×D3—122no—
684C2×D3—122no—
685C2×D3—122no—
686C2×D3—122no—
687C2×D3—122no—
688C3×C4—64no—
689C3×C4—122no—
690C3×C4—122no—
691C3×C4—122no—
692Dic3—24no—
693Dic3—42no—
694Dic3—42no—
695Dic3—42no—
696Dic3—68no—
697Dic3—64no—
698Dic3—64no—
699C32C2×#39411yescharacteristic, complemented, Sylow
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—28no—
707C23—28no—
708C23—28no—
709C23—44no—
710C23—44no—
711C23—44no—
712C23—44no—
713C23—94no—
714C23—182no—
715C23—182no—
716C23—182no—
717C23—182no—
718C23—182no—
719C23—182no—
720C23—188no—
721C23—188no—
722C23—188no—
723C23—364no—
724C23—364no—
725C23—364no—
726C23—364no—
727C23#380412yes—
728C23#380412yes—
729C23#380412yes—
730C23C2×#62614yes—
731C23C2×#62612yes—
732C23D3×#6712yes—
733C23#381112yes—
734C23#381112yes—
735C23C22×D3211yescharacteristic
736D4—1832no—
737C2×C4—34no—
738C2×C4—62no—
739C2×C4—62no—
740C2×C4—68no—
741C2×C4—62no—
742C2×C4—62no—
743C2×C4—62no—
744C2×C4—62no—
745C2×C4—62no—
746C2×C4—62no—
747C2×C4—62no—
748C2×C4—62no—
749C2×C4—62no—
750C2×C4—94no—
751C2×C4—124no—
752C2×C4—124no—
753C2×C4—124no—
754C2×C4—182no—
755C2×C4—182no—
756C2×C4—188no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—21no—
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—21no—
763C2×C3—21no—
764C2×C3—28no—
765C2×C3—48no—
766C2×C3—44no—
767C2×C3—44no—
768C2×C3#495918yescomplemented
769C2×C3#496118yescomplemented
770C2×C3C2×#88211yescharacteristic
771C2×C3C2×#88311yescharacteristic
772C2×C3C2×#88311yescharacteristic
773C2×C3C2×#88411yescharacteristic
774C2×C3C2×#88411yescharacteristic
775C2×C3C2×#88511yescharacteristic
776C2×C3C2×#88511yescharacteristic
777C2×C3C2×#88611yescharacteristic
778C2×C3C2×#92911yescharacteristic
779C2×C3C2×#93011yescharacteristic
780C2×C3C2×#93711yescharacteristic
781C2×C3C2×#93811yescharacteristic
782C2×C3C2×#93911yescharacteristic
783C2×C3C2×#93911yescharacteristic
784D3—128no—
785D3—124no—
786D3—124no—
787C22—24no—
788C22—24no—
789C22—24no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—416no—
795C22—184no—
796C22—184no—
797C22—184no—
798C22—362no—
799C22—362no—
800C22—362no—
801C22—362no—
802C22—3616no—
803C22#6395314yes—
804C22#6395814yes—
805C22#6396614yes—
806C22#6397114yes—
807C22#6397514yes—
808C22#6397814yes—
809C22#6398114yes—
810C22C2×#380411yescharacteristic
811C22C2×#380411yescharacteristic
812C22C2×#380411yescharacteristic
813C22C22×#62611yescharacteristic
814C22C2×D3×#6711yescharacteristic
815C22C2×#381111yescharacteristic
816C22C2×#381111yescharacteristic
817C4—64no—
818C4—122no—
819C4—122no—
820C4—122no—
821C4—184no—
822C3—21no—
823C3C2×#496111yescharacteristic, complemented
824C3C2×#495911yescharacteristic, complemented
825C2—44no—
826C2—364no—
827C2#1059171218yesdirect product factor
828C2C2×#6395311yescharacteristic
829C2C2×#6395811yescharacteristic
830C2C2×#6396611yescharacteristic
831C2C2×#6397111yescharacteristic
832C2C2×#6397511yescharacteristic
833C2C2×#6397811yescharacteristic
834C2C2×#6398111yescharacteristic
subgroupG/H
centerC24C2×D32
commutator, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC25×C32C22
socleC24×C32C23
prime radicalC23×#638C2
hypercenterC25D32
hypocenterC32C2×#394
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C25

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C22×C3×#217C2semidirect
3. C22×C3×#217C2semidirect
4. C22×Dic3⋊Dic3C2semidirect
5. C22×#3722C2semidirect
6. C22×#3722C2semidirect
7. #10591712C2direct (N × H)
8. C2×#63579C2semidirect
24. C2×C3×#217C22semidirect
25. C2×C3×#217C22semidirect
27. C2×Dic3⋊Dic3C22semidirect
30. C2×#3722C22semidirect
31. C2×#3722C22semidirect
32. #63579C22semidirect
38. C22×#217D3semidirect
39. C22×#217D3semidirect
86. C22×C3×Dic3D4semidirect
132. C2×#217C2×D3semidirect
133. C2×#217C2×D3semidirect
204. C2×C3×Dic3C2×D4semidirect
315. C22×Dic3#67semidirect
541. C2×Dic3C2×#67semidirect
543. C2×C32#394semidirect
699. C32C2×#394semidirect
768. C2×C3#4959semidirect
769. C2×C3#4961semidirect
823. C3C2×#4961semidirect
824. C3C2×#4959semidirect
827. C2#10591712direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C23×#6382
C22×C3×#2172
C22×Dic3⋊Dic32
C22×#37222
#105917122
C2×#635792
C2×#49593
C2×#49613